[/
  Copyright 2011 - 2020 John Maddock.
  Copyright 2013 - 2019 Paul A. Bristow.
  Copyright 2013 Christopher Kormanyos.

  Distributed under the Boost Software License, Version 1.0.
  (See accompanying file LICENSE_1_0.txt or copy at
  http://www.boost.org/LICENSE_1_0.txt).
]

[section:tommath_rational tommath_rational]

`#include <nil/crypto3/multiprecision/tommath.hpp>`

   namespace boost{ namespace multiprecision{

   typedef rational_adpater<tommath_int>        tommath_rational;
   typedef number<tommath_rational >         tom_rational;

   }} // namespaces

The `tommath_rational` back-end is used via the typedef `nil::crypto3::multiprecision::tom_rational`.  It acts as a thin wrapper around
`boost::rational<tom_int>`
to provide a rational number type that is a drop-in replacement for the native C++ number types, but with unlimited precision.

The advantage of using this type rather than `boost::rational<tom_int>` directly, is that it is expression-template enabled,
greatly reducing the number of temporaries created in complex expressions.

There are also non-member functions:

   tom_int numerator(const tom_rational&);
   tom_int denominator(const tom_rational&);

which return the numerator and denominator of the number.

Things you should know when using this type:

* Default constructed `tom_rational`s have the value zero (this the inherited Boost.Rational behavior).
* Division by zero results in a `std::overflow_error` being thrown.
* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be
interpreted as a valid rational number.
* No changes are made to [tommath]'s global state, so this type can safely coexist with other [tommath] code.
* Performance of this type has been found to be pretty poor - this need further investigation - but it appears that Boost.Rational
needs some improvement in this area.

[h5 Example:]

[mp_rat_eg]

[endsect] [/section:tommath_rational tommath_rational]
